Model parameter extraction

Fig. 23, Integrated density and step-height-dependent model parameter extraction approach. The outer loop finds the planarization length that best captures the density dependence, while the inner loop find the step-height model parameters that best explain up and down area polish data [48].

Finally, we have proposed a model framework for copper CMP simulation. Characterization methods (masks with physical, electrical test structures) for single- and multi-level pattern-dependencies are also under development, and we are pursuing ways to overcome challenges in model parameter extraction and validation. 

Model parameter extraction. The experiment data are fit against the CMP model. A set of optimized model parameters are chosen to minimize the fitting error, that is, mismatch between model calculation and experiment result. The model is cahbrated once the optimized model parameters are extracted. 

A battery test with the test profile in Fig. 3 was conducted on the battery. Mixed charging and discharging current with different current rates were performed to sufficiently excite the battery for model parameter extraction. The errors between the measured terminal voltage and the model output terminal voltage were... 

Table 1.3 Power law exponent s for the frequency-dependent component of the ac conductivity measured on different days and the FITC model parameters extracted from the dc component for the sintered Sn02 nanoparticle film. A, w and

In a regression approach to material characterization, a statistical model which describes the relation between measurements and the material property is formulated and unknown model parameters are estimated from experimental data. This approach is attractive because it does not require a detailed physical model, and because it automatically extracts and optimally combines important features. Moreover, it can exploit the large amounts of data available. 

The equivalent TMB operating conditions and model parameters for the reference case were given in Table 9-1 and Fig. 9-9 presents the corresponding steady state internal concentration profdes obtained with the simulation package. The extract and raffinate purities were 97.6 % and 99.3 %, respectively the recoveries were 99.3 % and 97.6 % for the extract and raffinate streams. The solvent consumption was 1.19 L g and the productivity was 68.2 g/day - L of bed. 

The two BCs of the TAP reactor model (1) the reactor inlet BC of the idealization of the pulse input to tiie delta function and (2) the assumption of an infinitely large pumping speed at the reactor outlet BC, are discussed. Gleaves et al. [1] first gave a TAP reactor model for extracting rate parameters, which was extended by Zou et al. [6] and Constales et al. [7]. The reactor equation used here is an equivalent form fi om Wang et al. [8] that is written to be also applicable to reactors with a variable cross-sectional area and diffusivity. The reactor model is based on Knudsen flow in a tube, and the reactor equation is the diffusion equation ... 

The material covered in the appendices is provided as a supplement for readers interested in more detail than could be provided in the main text. Appendix A discusses the derivation of the spectral relaxation (SR) model starting from the scalar spectral transport equation. The SR model is introduced in Chapter 4 as a non-equilibrium model for the scalar dissipation rate. The material in Appendix A is an attempt to connect the model to a more fundamental description based on two-point spectral transport. This connection can be exploited to extract model parameters from direct-numerical simulation data of homogeneous turbulent scalar mixing (Fox and Yeung 1999). 

These equations describe an unheated transistor and were verified for a device with no backside etching (no membrane). The modelling parameters were provided by the manufacturer, whereas the value of the threshold voltage was taken from wafer map data. The channel length modulation parameter. A, had to be extracted from measurement data. The discrepancy between simulated and measured source-drain saturation current, fsd,sat> for a transistor embedded in the bulk silicon was less than 1%, which confirmed the vaHdity of the model assumptions. 

Since the uncertainty in model parameters Hmits the model accuracy, a deviation of 10% is generally considered a very good result. The measurements therefore demonstrate the validity of the presented model, in particular when considering that the temperature-dependent parameters are extracted from data that are only valid in a temperature range between 0 °C and 100 °C. 

Fitting model predictions to experimental observations can be performed in the Laplace, Fourier or time domains with optimal parameter choices often being made using weighted residuals techniques. James et al. [71] review and compare least squares, stochastic and hill-climbing methods for evaluating parameters and Froment and Bischoff [16] summarise some of the more common methods and warn that ordinary moments matching-techniques appear to be less reliable than alternative procedures. References 72 and 73 are studies of the errors associated with a selection of parameter extraction routines. 

Parameters Extracted from Fitting SRC Model to Data Obtained from MbCO as well as from tbe Protobeme Alone Embedded in Various Solvents... 

Recall that the secondary-structure model for RNA is a model - and a crude one at that. It neglects pseudo knots and other tertiary interactions, does not take deviations from the additive nearest neighbor energy model into account, and is based on thermodynamic parameters extracted from melting experiments by means of multidimensional fitting procedures. Thus, you cannot expect perfect predictions for each individual sequence. Rather, the accuracy is on the order of 50% of the base pairs for the minimum free energy structure. 

A detailed transport model for resist dissolution has been developed (169). In conjunction with standard ellipsometric equations describing multilayer films, the model provides quantitative agreement with the observed traces from the in situ ellipsometer. Model parameters are thus extracted, and their significance in terms of molecular structures of the system can be established. This model can then be extended for predictive purposes in the design and selection of resist materials. 

When one builds a quantitative model using PCR or PLS, one is often not aware that the model parameters that are generated present an opportunity to learn some useful information. Information extracted from these model parameters cannot only be used to better understand the process and measurement system, but also lead to improved confidence in the validity of the quantitative method itself. 

In order to illustrate the ability to extract valuable information from such model parameters, a data set containing NIR transmission spectra of a series of polymer films will be used. In this example, films were extruded from seven different polymer blends, each of which was formulated using different ratios of high-density polyethylene (HDPE) and low-density polyethylene (LDPE). NIR spectra were then obtained for four or five replicate film samples at each blend composition. Table 8.9 lists the HDPE contents of the seven different formulations, and Figure 8.27 shows the NIR spectra that were obtained. Note that there is very little visible separation between the spectra. However, this does not mean that there is little information in the spectra, as will be shown below. 

The optimal model is determined by finding the minimum error between the extracted concentrations and the reference concentrations. Cross-validation is also used to determine the optimal number of model parameters, for example, the number of factors in PLS or principal components in PCR, and to prevent over- or underfitting. Technically, because the data sets used for calibration and validation are independent for each iteration, the validation is performed without bias. When a statistically sufficient number of spectra are used for calibration and validation, the chosen model and its outcome, the b vector, should be representative of the data. 

An Earth example not previously discussed deals with the roles of temperature and pressure on the density of ice cores (Marion and Jakubowski 2004). Gow (1971) has shown that the density of deep ice cores under pressure relaxes elastically as soon as the cores are extracted. In Fig. 5.9, we used our model parameters to calculate how the density of an ice core from Antarctica (Gow et al. 1968 Gow 1971) would vary with core temperature at 1 atm, which is what is measured at the surface with corrections for temperature, to the same core under both temperature and pressure constraints. At 1 atm pressure, the core density changes linearly with temperature (Fig. 5.9), in agreement with our model (Fig. 3.2) and the Gow (1971) results (see his table 1). In contrast, the density of the ice core subjected to both temperature... 

Quantitative Predictions. In this section we use the riser data to determine intrinsic activity and coking parameters (kj, Aj) in the model, and then predict MAT and FFB conversion and coke yields. Typically, we will have either the MAT or FFB activity and coke information and the task is to predict the riser performance. As the models use intrinsic parameters, it is immaterial which test information is available. The intrinsic parameters can be easily extracted by fitting the data to the appropriate reactor model. We will use the riser data as it gives the intrinsic information directly. The fitted rate parameters are summarized in Table III. The other model parameters, such as the activation energies, heats of reaction, the coke deactivation exponent, n, (also given in Table III), were estimated independently. The details of parameter estimates are described in the Appendix. 

The crystal-field parameters introduced in sect. 4.1 still contain all the structural information about the local environment. Therefore, a direct comparison of crystal-field parameters derived from different hosts, even with the same site symmetry, is not reasonable. In addition, the crystal-field parameters cannot be directly related to the distance and angle variations induced by the high-pressure application. Widely used models which extract the structural information from the crystal-field parameters are the angular-overlap (Jprgensen et al., 1963) and superposition model (Bradbury and Newman, 1967). In the case of f elements, the superposition model has been employed widely for the analysis of crystal-field parameters. 

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